Patentable/Patents/US-20250383858-A1
US-20250383858-A1

Multi-Phase Application Profiling and Compilation

PublishedDecember 18, 2025
Assigneenot available in USPTO data we have
Inventorsnot available in USPTO data we have
Technical Abstract

A computer implemented method manages application execution. A processor set monitors an execution of an application. The processor set collects current profile information for the application in response to detecting a phase change in the execution of the application. The processor set compares the current profile information with previously collected profile information for a number of existing profiles. The processor set patches the application to use an existing specialized body that is an optimized version of a general body that has been optimized for the previously collected profile information for an existing profile in the number of existing profiles in response to the current profile information matching the previously collected profile information for the existing profile.

Patent Claims

Legal claims defining the scope of protection, as filed with the USPTO.

1

. A computer implemented method for managing application execution, the computer implemented method comprising:

2

. The computer implemented method offurther comprising:

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. The computer implemented method offurther comprising:

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. The computer implemented method offurther comprising:

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. The computer implemented method offurther comprising:

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. The computer implemented method of, wherein collecting, by the processor set, the current profile information comprises:

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. The computer implemented method of, wherein the current profile information and the previously collected profile information comprises at least one of a function call, a branch, a system call, or an expected value.

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. The computer implemented method of, wherein the phase change is indicated by at least one of a software event, a hardware event, or an external condition.

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. A computer system comprising:

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. The computer system of, wherein the program instructions, collectively stored in the set of one or more storage media, further causes the processor set to perform the following computer operations:

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. The computer system of, wherein the program instructions, collectively stored in the set of one or more storage media, further causes the processor set to perform the following computer operations:

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. The computer system of, wherein the program instructions, collectively stored in the set of one or more storage media, further causes the processor set to perform the following computer operations:

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. The computer system of, wherein the program instructions, collectively stored in the set of one or more storage media, further causes the processor set to perform the following computer operations:

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. The computer system of, wherein in collecting the current profile information, wherein the program instructions, collectively stored in the set of one or more storage media, causes the processor set to perform the following computer operations:

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. The computer system of, wherein the current profile information and the previously collected profile information comprises at least one of a function call, a branch, a system call, or an expected value.

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. The computer system of, wherein the phase change is indicated by at least one of a software event, a hardware event, or an external condition.

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. A computer program product for managing application execution, the computer program product comprising:

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. The computer program product of, wherein the program instructions, collectively stored in the set of one or more storage media further cause the processor set to:

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. The computer program product of, wherein the program instructions, collectively stored in the set of one or more storage media further cause the processor set to:

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. The computer program product offurther comprising:

Detailed Description

Complete technical specification and implementation details from the patent document.

The disclosure relates generally to an improved computer system and more specifically to increasing the performance of applications with multiple phases.

Optimizing execution of code and application is performed for a number of different reasons. For example, the optimization can increase performance of an application. This increase in performance can have different aspects. For example, the performance can be related to execution time, resource consumption, throughput, reliability, latency, and other types of metrics.

For example, optimization can reduce execution time for tasks performed by applications such as those for gaming, financial trading, or other purposes. Additionally, a more efficient use of resources such as memory, disk, the processors, and network resources can occur. This efficient use can include a reduction in the use of memory, disk space, processor use, and network resources. In yet another example, the optimization can also increase user experience a lower latency that provides faster responsiveness to user requests.

In optimizing the code for an application, the code can be instrumented to generate information about the behavior of the code. The application with the instrumented code is run and profile information is collected from running this instrumented code. This profile information is used to identify one or more optimizations for the code. This code with the optimizations is then used in the application to increase performance of the application.

According to one illustrative embodiment, a computer implemented method manages application execution. A processor set monitors an execution of an application. The processor set collects current profile information for the application in response to detecting a phase change in the execution of the application. The processor set compares the current profile information with previously collected profile information for a number of existing profiles. The processor set patches the application to use an existing specialized body that is an optimized version of a general body that has been optimized for the previously collected profile information for an existing profile in the number of existing profiles in response to the current profile information matching the previously collected profile information for the existing profile. According to other illustrative embodiments, a computer system and a computer program product for managing application execution are provided.

Various aspects of the present disclosure are described by narrative text, flowcharts, block diagrams of computer systems and/or block diagrams of the machine logic included in computer program product (CPP) embodiments. With respect to any flowcharts, depending upon the technology involved, the operations can be performed in a different order than what is shown in a given flowchart. For example, again depending upon the technology involved, two operations shown in successive flowchart blocks may be performed in reverse order, as a single integrated step, concurrently, or in a manner at least partially overlapping in time.

A computer program product embodiment (“CPP embodiment” or “CPP”) is a term used in the present disclosure to describe any set of one, or more, storage media (also called “mediums”) collectively included in a set of one, or more, storage devices that collectively include machine readable code corresponding to instructions and/or data for performing computer operations specified in a given CPP claim. A “storage device” is any tangible device that can retain and store instructions for use by a computer processor. Without limitation, the computer-readable storage medium may be an electronic storage medium, a magnetic storage medium, an optical storage medium, an electromagnetic storage medium, a semiconductor storage medium, a mechanical storage medium, or any suitable combination of the foregoing. Some known types of storage devices that include these mediums include: diskette, hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or Flash memory), static random access memory (SRAM), compact disc read-only memory (CD-ROM), digital versatile disk (DVD), memory stick, floppy disk, mechanically encoded device (such as punch cards or pits/lands formed in a major surface of a disc) or any suitable combination of the foregoing. A computer-readable storage medium, as that term is used in the present disclosure, is not to be construed as storage in the form of transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide, light pulses passing through a fiber optic cable, electrical signals communicated through a wire, and/or other transmission media. As will be understood by those of skill in the art, data is typically moved at some occasional points in time during normal operations of a storage device, such as during access, de-fragmentation or garbage collection, but this does not render the storage device as transitory because the data is not transitory while it is stored.

With reference now to the figures in particular with reference to, a block diagram of a computing environment is depicted in accordance with an illustrative embodiment. Computing environmentcontains an example of an environment for the execution of at least some of the computer code involved in performing the inventive methods, such as application manager. In addition to application manager, computing environmentincludes, for example, computer, wide area network (WAN), end user device (EUD), remote server, public cloud, and private cloud. In this embodiment, computerincludes processor set(including processing circuitryand cache), communication fabric, volatile memory, persistent storage(including operating systemand application manager, as identified above), peripheral device set(including user interface (UI) device set, storage, and Internet of Things (IoT) sensor set), and network module. Remote serverincludes remote database. Public cloudincludes gateway, cloud orchestration module, host physical machine set, virtual machine set, and container set.

COMPUTERmay take the form of a desktop computer, laptop computer, tablet computer, smart phone, smart watch or other wearable computer, mainframe computer, quantum computer or any other form of computer or mobile device now known or to be developed in the future that is capable of running a program, accessing a network or querying a database, such as remote database. As is well understood in the art of computer technology, and depending upon the technology, performance of a computer-implemented method may be distributed among multiple computers and/or between multiple locations. On the other hand, in this presentation of computing environment, detailed discussion is focused on a single computer, specifically computer, to keep the presentation as simple as possible. Computermay be located in a cloud, even though it is not shown in a cloud in. On the other hand, computeris not required to be in a cloud except to any extent as may be affirmatively indicated.

PROCESSOR SETincludes one, or more, computer processors of any type now known or to be developed in the future. Processing circuitrymay be distributed over multiple packages, for example, multiple, coordinated integrated circuit chips. Processing circuitrymay implement multiple processor threads and/or multiple processor cores. Cacheis memory that is located in the processor chip package(s) and is typically used for data or code that should be available for rapid access by the threads or cores running on processor set. Cache memories are typically organized into multiple levels depending upon relative proximity to the processing circuitry. Alternatively, some, or all, of the cache for the processor set may be located “off chip.” In some computing environments, processor setmay be designed for working with qubits and performing quantum computing.

Computer-readable program instructions are typically loaded onto computerto cause a series of operational steps to be performed by processor setof computerand thereby effect a computer-implemented method, such that the instructions thus executed will instantiate the methods specified in flowcharts and/or narrative descriptions of computer-implemented methods included in this document (collectively referred to as “the inventive methods”). These computer-readable program instructions are stored in various types of computer-readable storage media, such as cacheand the other storage media discussed below. The program instructions, and associated data, are accessed by processor setto control and direct performance of the inventive methods. In computing environment, at least some of the instructions for performing the inventive methods may be stored in application managerin persistent storage.

COMMUNICATION FABRICis the signal conduction path that allows the various components of computerto communicate with each other. Typically, this fabric is made of switches and electrically conductive paths, such as the switches and electrically conductive paths that make up busses, bridges, physical input/output ports and the like. Other types of signal communication paths may be used, such as fiber optic communication paths and/or wireless communication paths.

VOLATILE MEMORYis any type of volatile memory now known or to be developed in the future. Examples include dynamic type random access memory (RAM) or static type RAM. Typically, volatile memoryis characterized by random access, but this is not required unless affirmatively indicated. In computer, the volatile memoryis located in a single package and is internal to computer, but, alternatively or additionally, the volatile memory may be distributed over multiple packages and/or located externally with respect to computer.

PERSISTENT STORAGEis any form of non-volatile storage for computers that is now known or to be developed in the future. The non-volatility of this storage means that the stored data is maintained regardless of whether power is being supplied to computerand/or directly to persistent storage. Persistent storagemay be a read only memory (ROM), but typically at least a portion of the persistent storage allows writing of data, deletion of data and re-writing of data. Some familiar forms of persistent storage include magnetic disks and solid state storage devices. Operating systemmay take several forms, such as various known proprietary operating systems or open source Portable Operating System Interface-type operating systems that employ a kernel. The code included in application managertypically includes at least some of the computer code involved in performing the inventive methods.

PERIPHERAL DEVICE SETincludes the set of peripheral devices of computer. Data communication connections between the peripheral devices and the other components of computermay be implemented in various ways, such as Bluetooth connections, Near-Field Communication (NFC) connections, connections made by cables (such as universal serial bus (USB) type cables), insertion-type connections (for example, secure digital (SD) card), connections made through local area communication networks and even connections made through wide area networks such as the internet. In various embodiments, UI device setmay include components such as a display screen, speaker, microphone, wearable devices (such as goggles and smart watches), keyboard, mouse, printer, touchpad, game controllers, and haptic devices. Storageis external storage, such as an external hard drive, or insertable storage, such as an SD card. Storagemay be persistent and/or volatile. In some embodiments, storagemay take the form of a quantum computing storage device for storing data in the form of qubits. In embodiments where computeris required to have a large amount of storage (for example, where computerlocally stores and manages a large database) then this storage may be provided by peripheral storage devices designed for storing very large amounts of data, such as a storage area network (SAN) that is shared by multiple, geographically distributed computers. IoT sensor setis made up of sensors that can be used in Internet of Things applications. For example, one sensor may be a thermometer and another sensor may be a motion detector.

NETWORK MODULEis the collection of computer software, hardware, and firmware that allows computerto communicate with other computers through WAN. Network modulemay include hardware, such as modems or Wi-Fi signal transceivers, software for packetizing and/or de-packetizing data for communication network transmission, and/or web browser software for communicating data over the internet. In some embodiments, network control functions and network forwarding functions of network moduleare performed on the same physical hardware device. In other embodiments (for example, embodiments that utilize software-defined networking (SDN)), the control functions and the forwarding functions of network moduleare performed on physically separate devices, such that the control functions manage several different network hardware devices. Computer-readable program instructions for performing the inventive methods can typically be downloaded to computerfrom an external computer or external storage device through a network adapter card or network interface included in network module.

WANis any wide area network (for example, the internet) capable of communicating computer data over non-local distances by any technology for communicating computer data, now known or to be developed in the future. In some embodiments, the WANmay be replaced and/or supplemented by local area networks (LANs) designed to communicate data between devices located in a local area, such as a Wi-Fi network. The WAN and/or LANs typically include computer hardware such as copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and edge servers.

END USER DEVICE (EUD)is any computer system that is used and controlled by an end user (for example, a customer of an enterprise that operates computer), and may take any of the forms discussed above in connection with computer. EUDtypically receives helpful and useful data from the operations of computer. For example, in a hypothetical case where computeris designed to provide a recommendation to an end user, this recommendation would typically be communicated from network moduleof computerthrough WANto EUD. In this way, EUDcan display, or otherwise present, the recommendation to an end user. In some embodiments, EUDmay be a client device, such as thin client, heavy client, mainframe computer, desktop computer and so on.

REMOTE SERVERis any computer system that serves at least some data and/or functionality to computer. Remote servermay be controlled and used by the same entity that operates computer. Remote serverrepresents the machine(s) that collect and store helpful and useful data for use by other computers, such as computer. For example, in a hypothetical case where computeris designed and programmed to provide a recommendation based on historical data, then this historical data may be provided to computerfrom remote databaseof remote server.

PUBLIC CLOUDis any computer system available for use by multiple entities that provides on-demand availability of computer system resources and/or other computer capabilities, especially data storage (cloud storage) and computing power, without direct active management by the user. Cloud computing typically leverages sharing of resources to achieve coherence and economies of scale. The direct and active management of the computing resources of public cloudis performed by the computer hardware and/or software of cloud orchestration module. The computing resources provided by public cloudare typically implemented by virtual computing environments that run on various computers making up the computers of host physical machine set, which is the universe of physical computers in and/or available to public cloud. The virtual computing environments (VCEs) typically take the form of virtual machines from virtual machine setand/or containers from container set. It is understood that these VCEs may be stored as images and may be transferred among and between the various physical machine hosts, either as images or after instantiation of the VCE. Cloud orchestration modulemanages the transfer and storage of images, deploys new instantiations of VCEs and manages active instantiations of VCE deployments. Gatewayis the collection of computer software, hardware, and firmware that allows public cloudto communicate through WAN.

Some further explanation of virtualized computing environments (VCEs) will now be provided. VCEs can be stored as “images.” A new active instance of the VCE can be instantiated from the image. Two familiar types of VCEs are virtual machines and containers. A container is a VCE that uses operating-system-level virtualization. This refers to an operating system feature in which the kernel allows the existence of multiple isolated user-space instances, called containers. These isolated user-space instances typically behave as real computers from the point of view of programs running in them. A computer program running on an ordinary operating system can utilize all resources of that computer, such as connected devices, files and folders, network shares, CPU power, and quantifiable hardware capabilities. However, programs running inside a container can only use the contents of the container and devices assigned to the container, a feature which is known as containerization.

PRIVATE CLOUDis similar to public cloud, except that the computing resources are only available for use by a single enterprise. While private cloudis depicted as being in communication with WAN, in other embodiments a private cloud may be disconnected from the internet entirely and only accessible through a local/private network. A hybrid cloud is a composition of multiple clouds of different types (for example, private, community or public cloud types), often respectively implemented by different vendors. Each of the multiple clouds remains a separate and discrete entity, but the larger hybrid cloud architecture is bound together by standardized or proprietary technology that enables orchestration, management, and/or data/application portability between the multiple constituent clouds. In this embodiment, public cloudand private cloudare both part of a larger hybrid cloud.

CLOUD COMPUTING SERVICES AND/OR MICROSERVICES: Public cloudand private cloudare programmed and configured to deliver cloud computing services and/or microservices (not separately shown in). Unless otherwise indicated, the word “microservices” shall be interpreted as inclusive of larger “services” regardless of size. Cloud services are infrastructure, platforms, or software that are typically hosted by third-party providers and made available to users through the internet. Cloud services facilitate the flow of user data from front-end clients (for example, user-side servers, tablets, desktops, laptops), through the internet, to the provider's systems, and back. In some embodiments, cloud services may be configured and orchestrated according to as “as a service” technology paradigm where something is being presented to an internal or external customer in the form of a cloud computing service. As-a-Service offerings typically provide endpoints with which various customers interface. These endpoints are typically based on a set of APIs. One category of as-a-service offering is Platform as a Service (PaaS), where a service provider provisions, instantiates, runs, and manages a modular bundle of code that customers can use to instantiate a computing platform and one or more applications, without the complexity of building and maintaining the infrastructure typically associated with these things. Another category is Software as a Service (SaaS) where software is centrally hosted and allocated on a subscription basis. SaaS is also known as on-demand software, web-based software, or web-hosted software. Four technological sub-fields involved in cloud services are: deployment, integration, on demand, and virtual private networks.

The illustrative embodiments recognize and take into account one or more different considerations as described herein. Code in an application can be instrumented and the instrumented code can be compiled and run. This code can be one or more methods in the application. Instrumented code provides information about the behavior of the code that is running for the application. This information forms a profile for the application. A number of optimizations are identified for the code using the information in the profile. The code can be modified with these optimizations to form optimized code. The application is compiled with the optimized code and run. For example, when the code are in methods, this profiling and optimization can be run by a just in time (JIT) compiler.

Current techniques do not take into account that applications can have multiple phases. For example, an application that is a scientific program can have a calculation phase and an analysis phase. As another example, an artificial intelligence system can have a model and data loading phase and a calculating phase that generates results. Additionally, a phase can be based on the time of day. A function may be different for different times of the day. For example, a webpage can be different languages based on the time of day. The webpage may be in a first language during a first part of the day and in a second language during a second part of the day.

With multiphase applications, optimizations of code using a single profile can result in suboptimal performance of the code in each phase of the application. As a result, the entire program may run with a lower level of performance.

Thus, illustrative examples provide a computer implemented method, apparatus, system, and computer program product for managing execution of an application. For example, a computer implemented method runs an application, a processor set monitors an execution of an application. The processor set collects current profile information for the application in response to detecting a phase change in the execution of the application. The processor set compares the current profile information with previously collected profile information for existing profiles. The processor set patches the application to use an existing specialized body that is an optimized version of a general body that has been optimized for the previously collected profile information for an existing profile in the profiles in response to the current profile information matching the previously collected profile information for the existing profile.

In these examples, different optimizations of a body can be present and stored in association with profiles. These profiles are related to the phase of execution of an application. In these examples, when the current profile information sufficiently matches previously collected profile information for existing profiles, the optimized body for profile information in the existing profile matching the current profile information can be used to increase the performance of the application for that particular phase.

With reference now to, a block diagram of an application execution environment is depicted in accordance with an illustrative embodiment. In this illustrative example, application execution environmentincludes components that can be implemented in hardware such as the hardware shown in computing environmentin. Application management systemcan operate to manage the execution of application. In this example, applicationcan have multiple phasesthat occur during execution of application. With the occurrence of multiple phases, applicationis multiphase application.

In this illustrative example, application management systemcomprises application managerand computer system. Application manageris located in computer system. Application managermay be implemented using application managerin.

Application managercan be implemented in software, hardware, firmware or a combination thereof. When software is used, the operations performed by application managercan be implemented in program instructions configured to run on hardware, such as a processor unit. When firmware is used, the operations performed by application managercan be implemented in program instructions and data and stored in persistent memory to run on a processor unit. When hardware is employed, the hardware can include circuits that operate to perform the operations in application manager.

In the illustrative examples, the hardware can take a form selected from at least one of a circuit system, an integrated circuit, an application-specific integrated circuit (ASIC), a programmable logic device, or some other suitable type of hardware configured to perform a number of operations. With a programmable logic device, the device can be configured to perform the number of operations. The device can be reconfigured at a later time or can be permanently configured to perform the number of operations. Programmable logic devices include, for example, a programmable logic array, a programmable array logic, a field-programmable logic array, a field-programmable gate array, and other suitable hardware devices. Additionally, the processes can be implemented in organic components integrated with inorganic components and can be comprised entirely of organic components excluding a human being. For example, the processes can be implemented as circuits in organic semiconductors.

As used herein, “a number of” when used with reference to items, means one or more items. For example, “a number of operations” is one or more operations.

Further, the phrase “at least one of,” when used with a list of items, means different combinations of one or more of the listed items can be used, and only one of each item in the list may be needed. In other words, “at least one of” means any combination of items and number of items may be used from the list, but not all of the items in the list are required. The item can be a particular object, a thing, or a category.

For example, without limitation, “at least one of item A, item B, or item C” may include item A, item A and item B, or item B. This example also may include item A, item B, and item C or item B and item C. Of course, any combination of these items can be present. In some illustrative examples, “at least one of” can be, for example, without limitation, two of item A; one of item B; and ten of item C; four of item B and seven of item C; or other suitable combinations.

Computer systemis a physical hardware system and includes one or more data processing systems. When more than one data processing system is present in computer system, those data processing systems are in communication with each other using a communications medium. The communications medium can be a network. The data processing systems can be selected from at least one of a computer, a server computer, a tablet computer, or some other suitable data processing system.

As depicted, computer systemincludes processor setthat is capable of executing program instructionsimplementing processes in the illustrative examples. In other words, program instructionsare computer-readable program instructions. Processor setis an example of processor setin.

As used herein, a processor unit in processor setis a hardware device and is comprised of hardware circuits such as those on an integrated circuit that respond to and process instructions and program code that operate a computer. Processor setcan be a number of processor units that can be implemented using processor setin. The processor units can also be referred to as computer processors. When processor setexecutes program instructionsfor a process, processor setcan be one or more processor units that are in the same computer or in different computers. In other words, the process can be distributed between processor units in processor seton the same or different computers in computer system. Further, processor setcan include the same type or different types of processor units. For example, processor setcan be selected from at least one of a single core processor, a dual-core processor, a multi-processor core, a general-purpose central processing unit (CPU), a graphics processing unit (GPU), a digital signal processor (DSP), or some other type of processor unit.

Although not shown, processor setcan also include other components in addition to the processor units or processing circuitry. For example, processor setcan also include a cache or other components used with processor units or other processing circuitry.

In this illustrative example, application manageroperates to manage the execution of application. For example, the application managermonitors an execution of application. In this example, the monitoring is to detect a phase change between multiple phasesthat can occur in application.

Application managercollects current profile informationfor applicationin response to detecting phase changein the execution of the application. In this example, profile information comprises at least one of a function call, a branch, a system call, or an expected value, or other information about the behavior of an application.

In this illustrative example, in collecting current profile information, application managercompiles general bodywith profiling instrumentation to form instrumented body. In this illustrative example, a body is code that is executed. This body can be a method having a class, a function, a procedure, or some other construct that includes code for execution. In this example, general bodyis a version of the code that has not been optimized.

Application managerpatches applicationto call instrumented body. Application managerruns applicationusing instrumented body. Application managercollects current profile informationin response to running applicationusing instrumented body.

In this example, application managercompares current profile informationwith previously collected profile informationfor existing profiles. Further in this example, application managerpatches (updates) applicationto use an existing specialized bodythat is an optimized version of a general bodythat has been optimized for previously collected profile informationfor existing profilein the existing profilesin response to current profile informationmatching previously collected profile informationfor existing profiles. In this example, the calls patched in applicationare to general body. The patching changes a call to use existing specialized bodyinstead of general body.

Application managercan then continue execution of applicationusing existing specialized body. For example, application managerruns applicationthat has impact using existing specialized body. In this example, the pattern can occur as calls for the body are encountered. In some cases, the entire application can be patched at the same time to direct calls to the body to existing specialized body. For example, the calls in applicationcan be to general bodyfor which existing specialized bodyis an optimized version of general body.

In another example, current profile informationdoes not match any of the number of existing profiles. With this example, application managercompiles general bodywith optimization for current profile informationto form new specialized bodyin response to current profile informationnot matching previously collected profile informationfor the number of existing profiles. In other words, changes are made to general bodyto optimize the performance of the code in general bodyfor current profile information.

Application managerpatches applicationto use new specialized body. Further in this example, application managersaves current profile informationas part of previously collected profile information. Additionally, application managerassociates current profile informationwith new specialized body.

In these illustrative examples, the different specialized bodies are saved and not discarded in case these specialized can be used at a later time when phase changeoccurs. In these examples, applicationcan be patched to call different specialized bodies that are optimized for the profile in the current phase resulting from phase change. The performance of computer systemin executing applicationincreases with this optimization. Further, the profile information is saved in previously collected profile informationthat enables comparing current profile informationwith previously collected profile information.

In these illustrative examples, phase changeis indicated by at least one of a software event, a hardware event, or an external condition. For example, a software event that is phase changecan be a change in path frequency, a variable that is outside of a selected range, a variable that has a selected value or other software event. A hardware rate that can include, for example, a cache miss, a branch prediction, an interprocess communication (IPC), or other computing events. An external condition can be, for example, a particular time, a location, a weather condition, or some other condition that is external to the computer system.

Indication of phase changemay occur when one of these events occur greater than some threshold level or outside of the expected range. In this illustrative example, a body can be instrumented to generate an indication of when particular event or events occur for the body. An indication of the phase change may occur when one of these events occur greater than some threshold level or outside of the expected range.

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Publication Date

December 18, 2025

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